Make the interesting choice.
Improv is all about choices: you can be anyone, anywhere, anytime. What you shouldn't be is boring. Go ahead and make choices that are unusual, that are fresh and exciting, that we haven't seen before. You'll need conflict, so make a choice with possibilities for strong goals and action. You'll want to make use of physical comedy, so choose a situation that lets you move around.
One technique is to take the first thing that comes to your mind and ignore it, since your first reaction to a setting or situation is probably going to be something stereotypical or expected. How many scenes have we seen where a restaurant was suggested as a location and we wind up with a couple on their first date sitting at a table? (YesAnd.com's Asaf Ronen created a brilliant video on this very subject). Why not a chef and the health inspector? Or the restaurant owner and a tax collector. Or even an honest, emotional scene about a turning point between a couple with a history? It could be anything, stretch your imagination and have some fun. Don't settle for something typical, keep it interesting.
The thing about short form improv is: it's short. You don't have a lot of time to fool around, so go ahead and dive in to the scene. Don't waste your energy with waking up in the morning, getting into the car and going to your location, or making greetings to your scene partners ("Hi, Bob." "Hi, Phil. Nice day, huh." "Yep." "How you doin'?" "Can't complain...") start the scene in progress.
Start your relationships in progress, too. Nothing is more boring and gives you less to work with than a transaction scene -- the typical shop clerk and customer who don't know each other scene -- yet actors time and time again will start any scene with a retail setting with the same old "May I help you, sir?" If you were actually in a store and you heard one person say that to another, would you even bother listening in on their conversation? Why would you think your audience would be interested in that, then? Why not give yourself some emotional juice to work with by assuming a back story between these people and going from there? Same store, but: "Yeah, those jeans do make your butt look big. I'm sick of lying to you." or "Great nightgown! Why don't you wear that tonight and we can invite your sister over to join us?" or "I don't need school supplies, Mom, I'm dropping out!" Now, you'd want to listen.
A good set up is also vital as, to get all Aristotelian dramatic unity on 'ya, everything that follows in a scene should logically (albeit with twisted comedic logic) proceed from what came before. The most important choices you make will therefore be in the short time between receiving the game and audience suggestions and when you begin the scene. Once you are cooking along within a scene the time for active thinking has passed, and it's time to go with your instincts (honed through experience and rehearsal) and training.
The actor's job is justification.
I have written about the skill of justification elsewhere on this site, so here I'll just mention that you gotta have trust. Trust in your ability to make even the wildest choice or suggestion work. Anything can make sense, you just have to justify it.
Beware, however, about overjustification. You don't have to explain everything, and a little mystery or ambiguity is great. Don't be afraid to just be weird and go for it. Discover the whys of things as you go.
Picture a table in a restaurant. Can you see it? Chances are your image is a little fuzzy and undeveloped, the words bringing up a general impression of a place without detail, a sort of generic impression of restaurantness which may change from moment to moment as your mind wanders. Or, you may have pictured an actual restaurant from your past which may not have been what I had in mind at all, and might, in fact, have been incompatible with my vision if, say, I had asked you to go on to imagine examining the fine silverware while your image had been of a cheap burger joint.
Now, picture a five star French restaurant with starched white table cloths and stiff tux clad waiters. Or a southern bar-b-que shack with rough wooden picnic tables and a chalkboard menu. Or a Parisian sidewalk cafe with a view of the Eiffel Tower. Or a fast food stand, with plastic tables and plastic food. Or an International House of Pancakes. Or a British Pub. The more specific we are in our images the clearer they will be in our minds, and the more easily we transmit that specificity to the audience the clearer these images will be for them. And, the clearer they are, the more real they will be. It is by giving them these images in detail that the scene's reality will be shared by all.
So, be specific! This means making choices early on as to what those details will be, and sticking to them. There are no wrong decisions at this point, any specific choice will help to establish the Where in our minds, piece by piece, as we create the reality of this scene.
Suppose we have a scene that is to take place in an office. Well, what kind of office? A lawyer's office? An accountant's office? The oval office? It would be easy to simply establish a desk and a telephone and go from there, but if your conception of where you are is fuzzy it will certainly be so for the audience. Make a decision. These places will all be different in some way.
Let's make it a stockbroker's office. Before you say a word you should be able to communicate a sense of where you are through what you do. If you were suddenly transported to a broker's office you would probably be able to tell where you were just by looking around. The objects around you would give it away instantly. Just as a set designer and property master of the formal stage must decide what telling objects to include on the set, you must produce them in your space. And, just as an actor on the formal stage would never walk around the set before a scene and describe where he was and point out those objects, you must bring them to life by using them.
In our broker's office, there's probably a stock ticker or some sort of trading board. Read off some numbers. Much trading is done by computer these days, so go ahead and type in a trade. Pick up the telephone, dial, and advise your customer (Who? Detail again, "Mr. Trump, about Amalgamated Widget ...") to sell something. And, finally, open your window and invite your boss to come in off of the ledge. Now, we're in a stockbroker's office and no one had to come right out and say it. Specific details did the job painlessly.
Find the game.
Comedy depends on structure, and subverting structures (otherwise known as setting up expectations and then pulling a switch on the audience). The "rule of threes" is simply setting up a pattern (structure): 1) first example, 2) second example to set the pattern, 3) third example violates the expectation: Hitler, Stalin, and my Mother-in-law. When improvising an unstructured scene (one without much of a game to play off of) you have to "find the game" which really means just finding a structure to work within. Say you and a partner are playing two old people talking about your operations and you keep trying to top each other with a more comically horrific illness -- you've found a game of one upmanship. Or you're doing a scene with a health inspector who finds something only to have the chef come up with an outrageous explanation as to why conditions are like that -- you've found a justification game. Finding a game or structure to work within helps you set up the humor and gives you something to play. A scene without some sort of structure that's completely random usually goes nowhere.
One common game technique (the Upright Citizen's Brigade is famous for this) is to look for something in a scene that is slightly unusual, and then heighten that again and again, in a logical progression, until it reaches the absurd. This is especially effective when you continue to heighten the emotional connection between two people, who may go from dislike to actively trying to kill each other, or from attraction to the greatest love that ever was (and all in the course of a couple of minutes.)